TOKYO, Jan 8 (Reuters) - Japan's Nikkei share average is set to trade in range on Tuesday as investors remain cautious of the overbought market while yen's weakness has paused, but hopes for aggressive monetary easing support investor sentiment. Market players said the Nikkei was likely to trade between 10,500 to 10,700 on Tuesday, after ending down 0.8 percent to 10,599.01 on Monday. Nikkei futures in Chicago closed at 10,620, the same level Nikkei futures closed in Osaka. Analysts said that investors are expected to stay on the sidelines amid signs that the market is overbought, and there may be some profit-taking on the recent gains of exporters now that the weakening of the yen appears to have paused for the time being. "Market sentiment is still positive on the back of hopes for further easing, but buying may pause on bellwether shares while small caps may attract buying," said Hiroichi Nishi, general manager, SMBC Nikko Securities, adding that domestic retail investors have belatedly come back and have started buying small caps. The dollar traded at 87.42 yen, retreating from a 2-1/2 year high of 88.48 yen marked on Friday as robust appreciation over the past month had investors opting to book profits despite forecasts of further Bank of Japan stimulus later in the month. The Nikkei has risen about 22 percent since mid-November when Prime Minister Abe started calling for aggressive easing, taking the index deeper into overbought territory. Its 14-day relative strength index is at 78.09, far above 70 which is considered overbought and often indicates an imminent adjustment. The broader Topix dropped 0.8 percent on Monday. > Wall St edges off 5-year high, awaits earnings > Euro rises vs dollar ahead of ECB meeting, yen recovers > Yields edge up before $66 bln US debt sales > Gold falls, Fed asset purchases in focus > Oil firm, Brent's premium to U.S. narrowest since Sept STOCKS TO WATCH --Sharp Corp Sharp is considering new ways to shore up its crumbling finances but is not talking with Intel Corp at the moment about any investment from the U.S. chipmaker, executives from the Japanese firm said on Monday. Separately, the company had a better-than-expected operating profit for October-December, its top executive said on Monday, as the struggling Japanese consumer electronics giant scrambles to generate profits in the hopes of securing fresh financing. --Mitsui & Co Mitsui said on Monday that it will buy as much as a 30 percent stake in Spanish autoparts maker Gestamp Automocion's U.S. business for 300 million euros ($391 million). --JX Nippon Oil & Energy Corp Japan's biggest refiner, JX Nippon Oil, has cut contracted imports of Iranian crude this year by more than 10 percent from 2012 volumes, an industry source with direct knowledge of the matter said on Monday. --Cosmo Oil Co Cosmo has delayed the schedule for the restart of operations at its 220,000 barrels per day (bpd) Chiba refinery, company sources said on Monday. --Aozora Bank Ltd U.S. buyout firm Cerberus Capital Management LP will sell up to 591 million shares in Japanese lender Aozora, Aozora said in a government filing on Monday. --Nintendo Co Ltd's year-end sales of its Wii U games console were steady, though not as strong as when its Wii predecessor was first launched, the Japanese game maker's top executive told Reuters on Monday. --Honda Motor Co Ltd and its China joint ventures sold 63,264 vehicles in the country in December, down 19.2 percent from a year earlier, the Japanese automaker said on Monday. --Nissan Motor Co Ltd and its China joint venture sold 90,400 vehicles in China in December, down 24 percent from a year earlier, the Japanese automaker said on Monday.